Related papers: Space-Efficient Data Structures for Polyominoes an…
Given a simple polygon $P$ with $n$ vertices, we consider the problem of constructing a data structure for visibility queries: for any query point $q \in P$, compute the visibility polygon of $q$ in $P$. To obtain $O(\log n + k)$ query…
Temporal graphs represent interactions between entities over time. Deciding whether entities can reach each other through temporal paths is useful for various applications such as in communication networks and epidemiology. Previous works…
Given an $n$-bit array $A$, the succinct rank data structure problem asks to construct a data structure using space $n+r$ bits for $r\ll n$, supporting rank queries of form $\mathtt{rank}(x)=\sum_{i=0}^{x-1} A[i]$. In this paper, we design…
Semialgebraic graphs are graphs whose vertices are points in $\mathbb{R}^d$, and adjacency between two vertices is determined by the truth value of a semialgebraic predicate of constant complexity. We show how to harness polynomial…
Given an array A of $n$ elements, we wish to support queries for the most frequent and least frequent element in a subrange $[l, r]$ of $A$. We also wish to support updates that change a particular element at index $i$ or insert/ delete an…
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
We show that any embedding of a planar graph can be encoded succinctly while efficiently answering a number of topological queries near-optimally. More precisely, we build on a succinct representation that encodes an embedding of $m$ edges…
The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous important data structure problems, see Henzinger et al. [STOC'15]. In recent work, Larsen and…
We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution…
We consider the problem of compactly representing the Depth First Search (DFS) tree of a given undirected or directed graph having $n$ vertices and $m$ edges while supporting various DFS related queries efficiently in the RAM with…
There is growing interest in representing image data and feature descriptors using compact binary codes for fast near neighbor search. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes…
In this paper we investigate the problem of building a static data structure that represents a string s using space close to its compressed size, and allows fast access to individual characters of s. This type of structures was investigated…
We present a data structure that stores a sequence $s[1..n]$ over alphabet $[1..\sigma]$ in $n\Ho(s) + o(n)(\Ho(s){+}1)$ bits, where $\Ho(s)$ is the zero-order entropy of $s$. This structure supports the queries \access, \rank\ and \select,…
We propose different methods for alternative representation and visual augmentation of sheet music that help users gain an overview of general structure, repeating patterns, and the similarity of segments. To this end, we explored mapping…
The representation of a dynamic ordered set of $n$ integer keys drawn from a universe of size $m$ is a fundamental data structuring problem. Many solutions to this problem achieve optimal time but take polynomial space, therefore preserving…
We suggest a method for holding a dictionary data structure, which maps keys to values, in the spirit of Bloom Filters. The space requirements of the dictionary we suggest are much smaller than those of a hashtable. We allow storing n keys,…
Palindromes are strings that read the same forward and backward. The computation of palindromic structures within strings is a fundamental problem in string algorithms, being motivated by potential applications in formal language theory and…
Let $\kappa(s,t)$ denote the maximum number of internally disjoint $st$-paths in an undirected graph $G$. We consider designing a compact data structure that answers $k$-bounded node connectivity queries: given $s,t \in V$ return…
There are several known data structures that answer distance queries between two arbitrary vertices in a planar graph. The tradeoff is among preprocessing time, storage space and query time. In this paper we present three data structures…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…